TRANSITION PATH THEORY FOR MARKOV JUMP PROCESSES
TRANSITION PATH THEORY FOR MARKOV JUMP PROCESSES
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DOI：
10.1137/070699500
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发表时间：
2009-01-01
影响因子：
1.6
通讯作者：
Vanden-Eijnden, Eric
中科院分区：
文献类型：
--
作者：
Metzner, Philipp;Schuette, Christof;Vanden-Eijnden, Eric
转移路径理论（TPT）的框架是在离散状态空间上的连续时间马尔可夫链的背景下发展起来的。在遍历性假设下，TPT挑出状态空间中的任何两个子集，并分析相关反应轨迹的统计特性，即，随机步行者从一个子集过渡到另一个子集的那些轨迹。TPT给出的属性，如反应轨迹的概率分布，其概率电流和通量，以及它们的发生率和主要反应途径。本文详细阐述了马尔可夫链的TPT理论框架，并讨论了该理论与电阻网络理论以及Laplacian特征映射和扩散映射等数据分析工具的关系。还介绍了TPT中各种对象的数值计算的各种算法。最后，通过几个例子说明了理论和算法。
The framework of transition path theory (TPT) is developed in the context of continuous-time Markov chains on discrete state-spaces. Under assumption of ergodicity, TPT singles out any two subsets in the state-space and analyzes the statistical properties of the associated reactive trajectories, i.e., those trajectories by which the random walker transits from one subset to another. TPT gives properties such as the probability distribution of the reactive trajectories, their probability current and flux, and their rate of occurrence and the dominant reaction pathways. In this paper the framework of TPT for Markov chains is developed in detail, and the relation of the theory to electric resistor network theory and data analysis tools such as Laplacian eigenmaps and diffusion maps is discussed as well. Various algorithms for the numerical calculation of the various objects in TPT are also introduced. Finally, the theory and the algorithms are illustrated in several examples.